And if the top 4 teams advance from sectional you'd have 8 teams per regional.
My thought was to have 16 classed sectionals with 6-8 teams. The top two advance to 4 regionals of 8 teams, again with 2 advancing. The final 8 teams per class vie for state at a common site. Teams could be reseeded at each level, but with the representatives from the same sectional or regional separated (so basically you'd seed the top 3).
Benefits are that only 3 mats are needed so smaller schools could host sectional & regional; two teams advance so there's a better chance that the top 2 make it to state, and the whole tourney could be run in one week with sectionals on Tuesday, regionals on Thursday, and state on Saturday.